Periodic Functions: Meaning of 1-Periodicity

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SUMMARY

A function is defined as 1-periodic if it satisfies the condition f(x + n) = f(x) for all integers n. This means that the function repeats its values every unit interval along the x-axis. An example of a 1-periodic function is y = sin(2πx), which completes a full cycle over the interval of 1. Understanding periodicity is crucial for analyzing functions in trigonometry and calculus.

PREREQUISITES
  • Understanding of periodic functions
  • Basic knowledge of trigonometric functions
  • Familiarity with mathematical notation and concepts
  • Concept of integer sets in mathematics
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  • Study the properties of periodic functions in trigonometry
  • Explore the implications of different periods in functions
  • Learn about Fourier series and their relation to periodic functions
  • Investigate applications of periodic functions in real-world scenarios
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Mathematicians, students studying calculus and trigonometry, and anyone interested in the properties of periodic functions.

Rectifier
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I know that some functions are ## 2 \pi ## periodic but what does it mean that a function is ##1##-periodic.

Is it ##f(x+1n) = f(x)## where ## n \in \mathbb{Z} ## ?
 
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Sure. Same principle just with different numbers.
 
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For example, ##y = \sin(2\pi x)## has a period of 1.
 

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